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Chapter 10: Aggregate Demand I Building the IS-LM Model

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**1. **Chapter 10: Aggregate Demand I – Building the IS-LM Model

**2. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor In this chapter you will learn the IS curve, and its relation to
the Keynesian Cross
the Loanable Funds model
the LM curve, and its relation to
the Theory of Liquidity Preference
how the IS-LM model determines income and the interest rate in the short run when prices are fixed

**3. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Context Chapter 9 introduced the model of aggregate demand and aggregate supply.
Long run
flexible prices
output determined by factors of production & technology
unemployment equals its natural rate
Short run
prices fixed
output determined by aggregate demand
unemployment is negatively related to output

**4. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Context This chapter develops the IS-LM model, the theory that yields the aggregate demand curve and is used for the discussion of monetary and fiscal policies.
We focus on the short run and assume the price level is fixed.

**5. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor The Keynesian Cross A simple closed economy model in which income is determined by expenditure. (due to John Maynard Keynes)
Notation:
I = planned investment
E = C + I + G = planned expenditure
Y = real GDP = actual expenditure
Difference between actual & planned expenditure: unplanned inventory investment

**6. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Elements of the Keynesian Cross Stress that much of this model is very familiar to students: same consumption function as in previous chapters, same treatment of fiscal policy variables.
Note: In equilibrium, there’s no unplanned inventory investment. Firms are selling everything they had intended wanted to sell. Otherwise inventories would not be constant.
Stress that much of this model is very familiar to students: same consumption function as in previous chapters, same treatment of fiscal policy variables.
Note: In equilibrium, there’s no unplanned inventory investment. Firms are selling everything they had intended wanted to sell. Otherwise inventories would not be constant.

**7. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Graphing planned expenditure Why slope of E line equals the MPC:
With I and G exogenous, the only component of (C+I+G) that changes when income changes is consumption. A one-unit increase in income causes consumption---and therefore E---to increase by the MPC.
Recall from Chapter 3: the marginal propensity to consume, MPC, equals the increase in consumption resulting from a one-unit increase in disposable income. Since T is exogenous here, a one-unit increase in Y causes a one-unit increase in disposable income.
Why slope of E line equals the MPC:
With I and G exogenous, the only component of (C+I+G) that changes when income changes is consumption. A one-unit increase in income causes consumption---and therefore E---to increase by the MPC.
Recall from Chapter 3: the marginal propensity to consume, MPC, equals the increase in consumption resulting from a one-unit increase in disposable income. Since T is exogenous here, a one-unit increase in Y causes a one-unit increase in disposable income.

**8. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Graphing the equilibrium condition

**9. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor The equilibrium value of income The equilibrium point is the value of income where the curves cross.
Be sure your students understand why the equilibrium income appears on the horizontal and vertical axes. Answer: In equilibrium, E (which is measured on the vertical) = Y (which is measured on the horizontal).
The equilibrium point is the value of income where the curves cross.
Be sure your students understand why the equilibrium income appears on the horizontal and vertical axes. Answer: In equilibrium, E (which is measured on the vertical) = Y (which is measured on the horizontal).

**10. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor An increase in government purchases Explain why the vertical distance of the shift in the E curve equals ?G:
At any value of Y, an increase in G by the amount ?G causes an increase in E by the same amount.
At Y1, there is now an unplanned depletion of inventories, because people are buying more than firms are producing (E > Y).
Explain why the vertical distance of the shift in the E curve equals ?G:
At any value of Y, an increase in G by the amount ?G causes an increase in E by the same amount.
At Y1, there is now an unplanned depletion of inventories, because people are buying more than firms are producing (E > Y).

**11. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Solving for ?Y

**12. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor The government purchases multiplier Example: MPC = 0.8

**13. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor The government purchases multiplier Definition: the increase in income resulting from a €1 increase in G.
In this model, the G multiplier equals The textbook defines the multiplier as the increase in income resulting from a €1 increase in G. However, G is a real variable (as is Y ). So, if you wish to be more precise, then you might consider defining the multiplier as “the increase in income resulting from a one-unit increase in G.”
The textbook defines the multiplier as the increase in income resulting from a €1 increase in G. However, G is a real variable (as is Y ). So, if you wish to be more precise, then you might consider defining the multiplier as “the increase in income resulting from a one-unit increase in G.”

**14. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Why the multiplier is greater than 1 Initially, the increase in G causes an equal increase in Y: ?Y = ?G.
But ?Y ? ?C
? further ?Y
? further ?C
? further ?Y
So the final impact on income is much bigger than the initial ?G. Students are better able to understand this if given a more concrete example. For instance,
Suppose the government spends an additional €10 million on building bridges. Then, the revenues of bridge building firms increase by €10 million, all of which becomes income to somebody: some of it is paid to the workers and engineers and managers, the rest is profit – which is paid as dividends to shareholders. Hence, income rises €10 million (?Y = €10 million = ?G ). But, the people whose income just rose by €10 million are also consumers, and they will spend the fraction MPC of this extra income. Suppose MPC = 0.8, so C rises by €8 million. To be concrete, suppose they buy €8 million worth of Mercedes. Then, Mercedes sees its revenues increase by €8 million, all of which becomes income to somebody - either Mercedes’ workers, or its shareholders (?Y = €8 million). And what do they do with this extra income? They spend the fraction MPC (0.8) of it, causing ?C = €6.4 million (8/10 of €8 million). Suppose they spend all €6.4 million on Cadbury’s chocolate bars. Then, Cadbury Schweppes experiences a revenue increase of €6.4 million, which becomes income to somebody or other. (?Y = €6.4 million). So far, the total impact of the increase in bridge building on income is €10 million + €8 million + €6.4 million, which is much bigger than the government’s initial increase in spending. But this process continues, and the final impact on Y will be no less than €50 million (as the multiplier is 5). Students are better able to understand this if given a more concrete example. For instance,
Suppose the government spends an additional €10 million on building bridges. Then, the revenues of bridge building firms increase by €10 million, all of which becomes income to somebody: some of it is paid to the workers and engineers and managers, the rest is profit – which is paid as dividends to shareholders. Hence, income rises €10 million (?Y = €10 million = ?G ). But, the people whose income just rose by €10 million are also consumers, and they will spend the fraction MPC of this extra income. Suppose MPC = 0.8, so C rises by €8 million. To be concrete, suppose they buy €8 million worth of Mercedes. Then, Mercedes sees its revenues increase by €8 million, all of which becomes income to somebody - either Mercedes’ workers, or its shareholders (?Y = €8 million). And what do they do with this extra income? They spend the fraction MPC (0.8) of it, causing ?C = €6.4 million (8/10 of €8 million). Suppose they spend all €6.4 million on Cadbury’s chocolate bars. Then, Cadbury Schweppes experiences a revenue increase of €6.4 million, which becomes income to somebody or other. (?Y = €6.4 million). So far, the total impact of the increase in bridge building on income is €10 million + €8 million + €6.4 million, which is much bigger than the government’s initial increase in spending. But this process continues, and the final impact on Y will be no less than €50 million (as the multiplier is 5).

**15. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor An increase in taxes Experiment: An increase in taxes (note: the book does a decrease in taxes)
Suppose taxes are increased by ?T. Because I and G are exogenous, they do not change. However, C depends on (Y?T). So, at the initial value of Y, a tax increase of ?T causes disposable income to fall by ?T, which causes consumption to fall by MPC ? ?T. Because consumption falls, the change in C is negative: ?C = ? MPC ? ?T
C is part of planned expenditure. The fall in C causes the E line to shift down by the size of the initial drop in C.
At the initial value of output, there is now unplanned inventory investment: Sales have fallen below output, so the unsold output adds to inventory.
In this situation, firms will reduce production, causing total output, income, and expenditure to fall.
The new equilibrium is at Y2, where planned expenditure once again equals actual expenditure/output, and unplanned inventory investment is again equal to zero. Experiment: An increase in taxes (note: the book does a decrease in taxes)
Suppose taxes are increased by ?T. Because I and G are exogenous, they do not change. However, C depends on (Y?T). So, at the initial value of Y, a tax increase of ?T causes disposable income to fall by ?T, which causes consumption to fall by MPC ? ?T. Because consumption falls, the change in C is negative: ?C = ? MPC ? ?T
C is part of planned expenditure. The fall in C causes the E line to shift down by the size of the initial drop in C.
At the initial value of output, there is now unplanned inventory investment: Sales have fallen below output, so the unsold output adds to inventory.
In this situation, firms will reduce production, causing total output, income, and expenditure to fall.
The new equilibrium is at Y2, where planned expenditure once again equals actual expenditure/output, and unplanned inventory investment is again equal to zero.

**16. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Solving for ?Y

**17. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor The Tax Multiplier def: the change in income resulting from a €1 increase in T :

**18. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor The Tax Multiplier …is negative: An increase in taxes reduces consumer spending, which reduces equilibrium income.
…is greater than one (in absolute value): A change in taxes has a multiplier effect on income.
…is smaller than the govt spending multiplier: Consumers save the fraction (1-MPC) of a tax cut, so the initial boost in spending from a tax cut is smaller than from an equal increase in G.

**19. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Exercise: Use a graph of the Keynesian Cross to show the impact of an increase in investment on the equilibrium level of income/output. This in-class exercise not only gives students practice with the model, it also helps them understand the next topic: the IS curve.
This in-class exercise not only gives students practice with the model, it also helps them understand the next topic: the IS curve.

**20. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor The IS curve def: a graph of all combinations of r and Y that result in goods market equilibrium,
i.e. actual expenditure (output) = planned expenditure
The equation for the IS curve is:

**21. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Deriving the IS curve ?r ? ?I

**22. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Understanding the IS curve’s slope The IS curve is negatively sloped.
Intuition: A fall in the interest rate motivates firms to increase investment spending, which drives up total planned spending (E ).
To restore equilibrium in the goods market, output (Y ) must increase.

**23. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor The IS curve and the Loanable Funds model The IS curve can also be derived from the (hopefully now familiar) loanable funds model from chapter 3.
A decrease in income from Y1 to Y2 causes a fall in national saving. (Recall, S = Y-C-G)
The fall in saving causes a reduction in the supply of loanable funds. The interest rate must rise to restore equilibrium to the loanable funds market.
Now we can see where the IS curve gets its name:
When the loanable funds market is in equilibrium, investment = saving. The IS curve shows all combinations of r and Y such that investment (I) equals saving (S). Hence, “IS curve.”
The IS curve can also be derived from the (hopefully now familiar) loanable funds model from chapter 3.
A decrease in income from Y1 to Y2 causes a fall in national saving. (Recall, S = Y-C-G)
The fall in saving causes a reduction in the supply of loanable funds. The interest rate must rise to restore equilibrium to the loanable funds market.
Now we can see where the IS curve gets its name:
When the loanable funds market is in equilibrium, investment = saving. The IS curve shows all combinations of r and Y such that investment (I) equals saving (S). Hence, “IS curve.”

**24. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Fiscal Policy and the IS curve We can use the IS-LM model to see how fiscal policy (G and T ) can affect aggregate demand and output.
Let’s start by using the Keynesian Cross to see how fiscal policy shifts the IS curve…

**25. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Shifting the IS curve: ?G At any value of r, ?G ? ?E ? ?Y

**26. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Exercise: Shifting the IS curve Use the diagram of the Keynesian Cross or Loanable Funds model to show how an increase in taxes shifts the IS curve.

**27. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor The Theory of Liquidity Preference due to John Maynard Keynes.
A simple theory in which the interest rate is determined by money supply and money demand.

**28. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Money Supply The supply of real money balances is fixed: We are assuming a fixed supply of real money balances because
P is fixed by assumption (short-run), and M is an exogenous policy variable.
We are assuming a fixed supply of real money balances because
P is fixed by assumption (short-run), and M is an exogenous policy variable.

**29. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Money Demand Demand for real money balances: As we learned in chapter 4, the nominal interest rate is the opportunity cost of holding money (instead of bonds).
Here, we are assuming the price level is fixed, so ? = 0 and r = i. As we learned in chapter 4, the nominal interest rate is the opportunity cost of holding money (instead of bonds).
Here, we are assuming the price level is fixed, so ? = 0 and r = i.

**30. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Equilibrium The interest rate adjusts to equate the supply and demand for money:

**31. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor How the central bank raises the interest rate To increase r,
the central bank reduces M

**32. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor CASE STUDY: Volcker’s Monetary Tightening in the U.S. Late 1970s: ? > 10%
Oct 1979: new Federal Reserve Chairman Paul Volcker announces that monetary policy would aim to reduce inflation.
Aug 1979-April 1980: Federal Reserve reduces M/P 8.0%
Jan 1983: ? = 3.7% At this point, students have learned different theories about the effects of monetary policy on interest rates. This case study shows them that both theories are relevant, using a real-world example to remind students that the classical theory of chapter 4 applies in the long-run while the liquidity preference theory applies in the short run.
At this point, students have learned different theories about the effects of monetary policy on interest rates. This case study shows them that both theories are relevant, using a real-world example to remind students that the classical theory of chapter 4 applies in the long-run while the liquidity preference theory applies in the short run.

**33. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Volcker’s Monetary Tightening - II Since prices are sticky in the short run, the Liquidity Preference Theory predicts that both the nominal and real interest rates will rise in the short run. And in fact, both did. (However, the inflation rate was not zero, and in fact it increased, so the real interest rate didn’t rise as much as the nominal interest rate did during the period shown.)
In the long run, the Quantity Theory of Money says that the monetary tightening should reduce inflation. The Fisher Effect says that the fall in ? should cause an equal fall in i. By January of 1983 (which is “the long run” from the viewpoint of 1979), inflation and nominal interest rates had fallen. (However, they did not fall by equal amounts. This doesn’t contradict the Fisher Effect, though, as other economic changes caused movements in the real interest rate.)
The monetary contraction engineered by the Federal Reserve in the U.S. coincided in timing with the announcement of the Medium Term Financial Strategy (MTFS) of the Conservative government led by Margaret Thatcher in the UK. In the UK, inflation fell from 18% to less than 5% a year within a three year period. This occurred even though the government overshot the pre-announced expansion rates of M3 year after year – as output costs of disinflation turned out to be greater than anticipated.
About the data:
i = Fed Funds rate
% change in M/P from previous slide: I computed M1/CPI, then computed the percentage change in M1/CPI over the 8-month period beginning with the month in which Volcker became the Fed chairman, August 1979.
Source: http://www.federalreserve.gov/RELEASES/h15/data.htm
Since prices are sticky in the short run, the Liquidity Preference Theory predicts that both the nominal and real interest rates will rise in the short run. And in fact, both did. (However, the inflation rate was not zero, and in fact it increased, so the real interest rate didn’t rise as much as the nominal interest rate did during the period shown.)
In the long run, the Quantity Theory of Money says that the monetary tightening should reduce inflation. The Fisher Effect says that the fall in ? should cause an equal fall in i. By January of 1983 (which is “the long run” from the viewpoint of 1979), inflation and nominal interest rates had fallen. (However, they did not fall by equal amounts. This doesn’t contradict the Fisher Effect, though, as other economic changes caused movements in the real interest rate.)
The monetary contraction engineered by the Federal Reserve in the U.S. coincided in timing with the announcement of the Medium Term Financial Strategy (MTFS) of the Conservative government led by Margaret Thatcher in the UK. In the UK, inflation fell from 18% to less than 5% a year within a three year period. This occurred even though the government overshot the pre-announced expansion rates of M3 year after year – as output costs of disinflation turned out to be greater than anticipated.
About the data:
i = Fed Funds rate
% change in M/P from previous slide: I computed M1/CPI, then computed the percentage change in M1/CPI over the 8-month period beginning with the month in which Volcker became the Fed chairman, August 1979.
Source: http://www.federalreserve.gov/RELEASES/h15/data.htm

**34. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor The LM curve Now let’s put Y back into the money demand function:

**35. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Deriving the LM curve

**36. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Understanding the slope of the LM curve The LM curve is positively sloped.
Intuition: An increase in income raises money demand.
Since the supply of real balances is fixed, there is now excess demand in the money market at the initial interest rate.
The interest rate must rise to restore equilibrium in the money market.

**37. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor How ?M shifts the LM curve You might consider helping your students understand the analytical difference between looking at a shift as a horizontal shift and looking at it as a vertical shift.
We can think of the LM curve shift as a vertical shift:
When the central bank reduces M, the vertical distance of the shift tells us what happens to the equilibrium interest rate associated with a given value of income.
Or, we can think of the LM curve shifting horizontally:
When the central bank reduces M, the horizontal distance of the shift tells us what would have to happen to income to restore money market equilibrium at the initial interest rate. (The graphical analysis would be a little different than what’s depicted on this slide.)
You might consider helping your students understand the analytical difference between looking at a shift as a horizontal shift and looking at it as a vertical shift.
We can think of the LM curve shift as a vertical shift:
When the central bank reduces M, the vertical distance of the shift tells us what happens to the equilibrium interest rate associated with a given value of income.
Or, we can think of the LM curve shifting horizontally:
When the central bank reduces M, the horizontal distance of the shift tells us what would have to happen to income to restore money market equilibrium at the initial interest rate. (The graphical analysis would be a little different than what’s depicted on this slide.)

**38. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Exercise: Shifting the LM curve Suppose a wave of credit card fraud causes consumers to use cash more frequently in transactions.
Use the Liquidity Preference model to show how these events shift the LM curve. Answer:
This causes an increase in money demand. In the Liquidity Preference diagram, the money demand curve shifts up. Hence, at the the initial value of income, the interest rate must rise to restore equilibrium in the money market. As a result, the LM curve shifts up: each value of income (such as the initial income) is associated with a higher interest rate than before.
Answer:
This causes an increase in money demand. In the Liquidity Preference diagram, the money demand curve shifts up. Hence, at the the initial value of income, the interest rate must rise to restore equilibrium in the money market. As a result, the LM curve shifts up: each value of income (such as the initial income) is associated with a higher interest rate than before.

**39. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor The short-run equilibrium The short-run equilibrium is the combination of r and Y that simultaneously satisfies the equilibrium conditions in the goods & money markets:

**40. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor The Big Picture

**41. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Chapter summary Keynesian Cross
basic model of income determination
takes fiscal policy & investment as exogenous
fiscal policy has a multiplied impact on income.
IS curve
comes from Keynesian Cross: planned investment depends negatively on interest rate
shows all combinations of r and Y that equate planned expenditure with actual expenditure on goods & services on 1: to be more precise, any change in autonomous demand has a multiplied impact on income. (Autonomous demand includes autonomous private consumption and autonomous investment.)on 1: to be more precise, any change in autonomous demand has a multiplied impact on income. (Autonomous demand includes autonomous private consumption and autonomous investment.)

**42. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Chapter summary Theory of Liquidity Preference
basic model of interest rate determination
takes money supply & price level as exogenous
an increase in the money supply lowers the interest rate
LM curve
comes from Liquidity Preference Theory when money demand depends positively on income
shows all combinations of r and Y that equate demand for real money balances with supply

**43. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Chapter summary IS-LM model
Intersection of IS and LM curves shows the unique point (Y, r ) that satisfies equilibrium in both the goods and money markets.

**44. **© 2008 Worth Publishers Macroeconomics, European Edition Mankiw • Taylor Preview of Chapter 11 In Chapter 11, we will
use the IS-LM model to analyze the impact of policies and shocks
learn how the aggregate demand curve comes from IS-LM
use the IS-LM and AD-AS models together to analyze the short-run and long-run effects of shocks
learn about the Great Depression using our models